We will have the following:
[tex]\begin{gathered} d=vt+\frac{1}{2}at^2 \\ \\ \Rightarrow9.14=(0)t+\frac{1}{2}(9.8m/s^2)t^2\Rightarrow t^2=\frac{9.14}{4.9} \\ \\ \Rightarrow t=\sqrt{\frac{457}{245}}\Rightarrow t\approx1.365762103...s \end{gathered}[/tex]Now, we determine the velocity:
[tex]\begin{gathered} v_f=v_it+at \\ \\ \Rightarrow v_f=(0m/s)(\sqrt{\frac{457}{245}}s)+\frac{1}{2}(9.8m/s^2)(\sqrt{\frac{457}{245}}s)^2\Rightarrow v_f=\frac{457}{50}m/s \\ \\ \Rightarrow v_f=9.14m/s \end{gathered}[/tex]So, the velocity is 9.14 m/s.
